OFFSET
0,2
COMMENTS
This is row/column 9 of the Delannoy numbers array, A008288, which is the main entry for these numbers, listing many more properties. - Shel Kaphan, Jan 07 2023
LINKS
T. D. Noe, Table of n, a(n) for n = 0..1000
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
G.f.: (1+x)^9/(1-x)^10.
a(n) = (4*n^9+18*n^8+240*n^7+756*n^6+3612*n^5+7182*n^4+14360*n^3+14724*n^2+ 10134*n+2835)/2835. - Johannes W. Meijer, Jul 14 2013
a(0)=1, a(1)=19, a(2)=181, a(3)=1159, a(4)=5641, a(5)=22363, a(6)=75517, a(7)=224143, a(8)=598417, a(9)=1462563, a(n)=10*a(n-1)-45*a(n-2)+ 120*a(n-3)- 210*a(n-4)+252*a(n-5)-210*a(n-6)+120*a(n-7)-45*a(n-8)+ 10*a(n-9)- a(n-10). - Harvey P. Dale, Jul 25 2013
Sum_{n >= 1} (-1)^(n+1)/(n*a(n-1)*a(n)) = (1 - 1/2 + 1/3 - ... + 1/9) - log(2). - Peter Bala, Mar 23 2024
MATHEMATICA
CoefficientList[Series[(z + 1)^9/(z - 1)^10, {z, 0, 200}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 19 2011 *)
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {1, 19, 181, 1159, 5641, 22363, 75517, 224143, 598417, 1462563}, 40] (* Harvey P. Dale, Jul 25 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved